Evolution of phases in a shape memory alloy by local and global minimisations of a non convex potentials

International audienceA Shape Memory Alloy (SMA) is a mixture of martensite and austenite or only martensite or austenite. Austenite-martensite phase transformation leads to variations of composition. This transformation can appear by mechanical or thermal action. The characteristic pseudo-elastic behaviour appears from this modification in the material over certains conditions for which observe an hysteresis loop on the stress-strain relationship. This hysteresis can be influenced by several factors: thermal effect, dissipation, structural effect, existence of geometrical defect, etc. Here, we use a model taking the temperature, the deformation and the volumic proportions of austenite and martensite as state variables. We adopt, here, Fremond's modelling in the non dissipative case which gives a non monotonic stress-strain relationship. Some experiments (Chrysochoos et al., 1995) show that during room temperature test, dissipative effects are strongly dominated by effects resulting from temperature variations of material associated to the latent heat. In our case, after elimination of the volumic proportions of martensite, the bulk energy density is a non convex function